“”Pascal's wager: Believing in and searching for Kryptonite on the off chance that Superman exists and wants to kill you.

Pascal's wager is an argument based on probability theory and game theory as for why one should live as if God exists, even though this cannot be proved or disproved through reason. It was formulated by Blaise Pascal.[1]

Pascal's original formulation of the wager was written down as a fairly short paragraph in Pensées amongst several other notes that could be considered "wagers".[1] Its argument is rooted in game theory and that the best course of action is to believe in God regardless of any lack of evidence, because that option gives the biggest potential gains. Pascal's original text is long-winded and somewhat convoluted philosophy-speak,[2] but it can be distilled more simply:

If you believe in God and God does exist, you will be rewarded with eternal life in heaven: thus an infinite gain.

If you do not believe in God and God does exist, you will be condemned to remain in hell forever: thus an infinite loss.

If you believe in God and God does not exist, you will not be rewarded: thus a finite loss.

If you do not believe in God and God does not exist, you will not be rewarded, but you have lived your own life: thus a finite gain.

The gains and losses associated to outcomes 3 and 4 can be thought of as the opportunity costs of feigning belief and living in accordance with religious norms, since these are typically more restrictive than secular laws. These costs are finite because of human mortality. Mathematically, a finite gain or loss is negligible compared to an infinite gain or loss as would be incurred during an eternal afterlife. Therefore, Pascal concluded that it was a much better choice to believe in God rather than not. The Wager can also be seen in table form and it becomes clear that belief gives you a reward or (practically) nothing, while disbelief gives you punishment or nothing:

There are many problems with the reasoning in Pascal's Wager, as well as the unsavoury theological assumptions it makes. Like most arguments for the existence of God, it seems more about reassuring existing believers than converting non-believers. This is because in order to convince a non-believer, a theological argument must both prove that the god it argues for is the One True God and disprove all other possibilities. People lacking a belief can see the potential for multiple gods existing, in fact an infinite number, but believers are constrained by their existing view that there is their god or no god. Only in this latter case does the reasoning behind Pascal's Wager make any sense.

In Bayesian terms, this can be stated as saying non-believers attribute uniform prior probabilities to the existence of any particular god; all equal, and all infinitesimal. Pascal's Wager alone cannot update these probabilities as the reasoning applies only to the One True God out of an infinite number of possible gods. Without any further information to whittle this down, the odds of inadvertently worshiping the wrong god is a practical certainty. Only when the probability of a particular god existing increases does Pascal's Wager become useful, i.e., if one god could be assigned even a mere 1% chance of being the One True God, Pascal's Wager would present a clear benefit. Hence for anyone constrained by a bias towards a particular god, the Wager is far more clear cut and supportive of their belief.

The biggest irony of Pascal's Wager as far as Christian apologetics go is that even if it was otherwise completely sound it should then suddenly become a huge disincentive for convincing an unbiased party to worship YHWH specifically. By definition worshiping the Judeo-Christian God requires the worshipper to actively reject the existence of every other deity or potential deity thanks to the intolerance that is the First Commandment. In the absence of evidence for a specific deity, the theist-to-be would be better off directing some worship to one or more proposed deities that do not require exclusive worship. Pascal's Wager being a lynchpin of Christian apologetics (rather than being a shibboleth that must be denied at all costs) can be viewed as a case of cognitive dissonance engendered by Christianprivilege.

Pascal's wager makes a number of assumptions about reality, and a number of theological assumptions about the god it argues for. If any of these can be shown to either be false or undesirable, then the power of the Wager for determining one's actions and beliefs is severely weakened - indeed, the argument of the Wager can be reversed in some cases and it can argue for non-belief. These mostly stem from the theological implications of applying the Wager to belief in God, rather than the Game Theory attributes and decision making process presented.

This is the center of the problem. Pascal's wager assumes the afterlife can exist. However, all the evidence points towards a physical "person." What is the "soul" that exists after death? Such a part would have to be non-biological and non-modifiable, and no such part exists. Our thoughts, feelings, memories, and personality have been shown to come from interactions in the brain. They can also be affected by hormones, drugs, alcohol, head trauma, and other physical factors. No amount of philosophical babble can change this.

For an analogy: Let's say you (don't do this at home) dropped your computer from a 4 story building, ran over the remains 8 times, and dropped the remains in the ocean. Is the computer still running Windows in another plane of existence?

Perhaps the core of the Wager is that it assumes a human being has the ability to believe something by an act of will: not just to say one believes it but to actually, sincerely, believe it to be true. This is known as doxastic voluntarism; it is probable that most people lack the ability to do this deliberately. Beliefs are often involuntary; at the very least you (yes, you) possess an involuntary belief that you experience the world. Further, you have an involuntary belief that someone, somewhere, at some point in time, typed these very words. Similarly, it is difficult to believe things you know to be untrue. Consider how you would respond if someone told you to believe that the earth rested upon the back of a giant turtle. Even if you were inclined to, it is doubtful whether you really could genuinely believe it. Pascal attempted to "solve" this problem by saying that a nonbeliever should associate with believers, attend religious services, etc. until this inspires belief in them-essentially "fake it 'til you make it." The effectiveness of this is highly questionable though.

Freedom of action, however, is significantly different. This is something that people have considerably more free will to exert — so someone is free to worship God without believing. The question, therefore, is whether God has the ability to detect such a ruse or such belief in belief, or whether God would be happy to have people "fake" their beliefs in such a way.

Pascal's Wager must, at the very least, make one of the following assumptions:

That doxastic voluntarism is possible.

That God doesn't care if you "fake it".

One of those is known to be wrong, the other is theologically questionable, as discussed in the next section.

The Wager assumes that God will be impressed by, and happily reward, people who worship just to avoid Hell. An all-powerful (or very powerful) being would gain little from the mental allegiance of human beings. In the same way, a human persuading all the inhabitants of an anthill to worship you would be pretty pointless. The constant harangues and demands for worship by the Abrahamic god as stated in the Old Testament suggest that it might just be an ego thing.

If, as Pascal's Wager must assume, God is willing to punish good people simply for a lack of belief, this would preclude God being "good" by any sense that we understand the concept of "good" - and "good" is a necessary property of God. As it can be demonstrated on Earth that no single specific religion has a monopoly on good and moral people, a God that causes Pascal's Wager to be valid cannot be focused on spreading good around the world. Various responses to Pascal's Wager involve pointing out that to be at the constant beck-and-call of such a clearly evil being would be less preferable to hell, and so it is favourable to disbelieve.

The satirical fantasy writer Terry Pratchett had a version of Pascal's Wager in his book titled Hogfather: "Upon his death, the philosopher in question found himself surrounded by a group of angry gods with clubs. The last thing he heard was 'We're going to show you how we deal with Mister Clever Dick around here...'"

As an extension to the above, the Wager also assumes that a believer will only care about maximizing their own gains.

More troubling than this are occasions where you might theoretically be called upon to hurt someone else to advance your worship of the superior entity. This forms a flip-side to the argument that Pascal's Wager emphasizes belief over worthiness in that it suggests that outright evil people can gain reward and avoid punishment simply through belief. In the Old Testament there are numerous instances when worshipers had to kill and hurt others as commanded by God. In fact, there are occasions in which God was extremely displeased that they didn't take the abuse of fellow humans far enough. Even with the Pascal's Wager metric in place, one could argue that it's more moral to resist these commands for the sake of others even if it results in an infinite loss for you.

Again, it can be demonstrated on Earth that bad people who do bad things can still profess belief - Pascal therefore suggests they are worthy of infinite gain, and atheists cheekily suggest that being around those people in heaven isn't selling the whole belief thing to them very well.

Assuming that Pascal's Wager argues only for a Christian God (which narrows it even further from monotheistic and Abrahamic), there exists a number of sects and sub-sects that worship in different ways. Some require more stringent conditions for proper worship than others, and some of them downright contradict each other. The Wager alone doesn't really state how to get around this - presumably you just follow whatever Blaise Pascal did. So, if you don't do enough of the rituals required for proper worship you will still go to hell, not getting compensated for whatever piety-based losses you did incur.

Consider if God decided that the Mormon way of worshiping him was correct and that the Catholic way was incorrect. Then we are faced with having to believe in a God that waited for most of human history to reveal the correct way to pass the test! In fact, no matter which historical religion you choose, God has waited for most of human history to reveal the correct way to pass the test.

Alternatively, consider that none of the religions so far have it right. Behaving randomly would give you odds as good as joining any particular religion or religious sect. Indeed, since humans have no way of knowing which way is pleasing to God you may as well not even bother trying; a tiny gain plus going to Hell is better than a tiny loss plus still going to Hell.

Alternatively alternatively, consider that a previous religious did have it right in the past but then died out with no way to fully replicate their rituals. If, say, the Cathars knew the right way to get into heaven, the Albigensian Crusade pretty much permanently cut off that or any line of heavenly ascension -- thus making anyone's worship thereafter pointless.

One hidden assumption of Pascal's Wager is that the cost of worship is in fact infinitely small in some way. While this seems to be the case for limited human activities done in our mortal existence such as praying or church attendance, some religions in fact require a neverending payment in some form that will never ever be regained. This applies most notably to the Judeo-Christian religion; if the Book of Revelation is to be believed, once the elect actually ends up in Heaven they get brainwashed to worship the creator for eternity and lose a part of identity, never to be regained.

If you think that this would still be an axiomatically acceptable trade-off, ask how many people would be willing to trade an immortal existence of hedonism and pleasure in The Matrix if it meant forever being shielded from the truth. The number of people claiming that this is not a fair trade will be non-zero.

Utility is a measure of how good something is now - in economics it basically asks "how likely is someone to want it so much as to buy it". Marginal utility is a related concept that asks how this changes as you start to have more of something. Pascal's Wager and its fast-and-loose use of gains and losses is based around this concept. It assumes that going to hell will be infinitely miserable, while going to heaven would be infinitely pleasurable.

Consider that the afterlife lasts infinitely. Marginal utility states that the reward felt in the afterlife is certain to diminish over time, and that the punishment felt in hell will eventually turn from "screaming pain" to "meh" after a few million years or so - which is still tuppence compared to infinity. Therefore, on average, the marginal utility of any experiences in the afterlife are likely to be infinitesimal. Although this doesn't disprove the existence of an afterlife, it is a common argument against the desirability of an infinite afterlife and so affects the Wager's outcomes greatly. Consider a lottery payout of a million dollars... paid in installments of one dollar per year for example. Then consider a lottery payout of infinite dollars... paid in a single cent per century. The latter still gives you "infinite gain", but with a near-zero marginal utility.

This re-contextualisation quantifies the gain felt by believing in God considerably, and suggests the reward in the afterlife doesn't necessarily outweigh the finite losses felt in a mortal life.

Another common criticism is that the wager only deals with the traditional Judeo-Christian image of a god who rewards his followers. One could imagine a number of alternatives, many of which are believed in by parts of the world population. One possibility is that the true god is not Christian but Jewish, Muslim, Hindu, Buddhist, or a god of one of the many other existing religions. In his essay, Pascal basically dismisses all non-Christian religions as possibilities without showing why.

Another possibility is that the true god is a perverse god who would damn his supporters and reward unbelievers simply for the sake of irony,[3] or the Maltheistic idea that "gods" are spiritual entities who eat their worshippers' souls after their deaths.[4]

Also, the wager only allows for one true god. Should there be more than one (such as in the Greek and Roman mythologies), a follower of Pascal may offend a powerful god by only worshipping a weaker one, leading to his damnation despite his worship.

The wager also assumes that once you've passed the point of no return and have received your just deserts, the deity will never change its mind in the future -- otherwise it's not really an infinite loss/gain, is it? Yet there are instances in mythology of exceptional individuals experiencing a reversal of heavenly fate. Quite famously Satan and to a lesser extent Adam got a free ride for infinite gain until they displeased God. There's also no guarantee that hell will forever be be infinitely miserable either. Satan for example could turn you into a rockin' demon or mellow out and remodel the underworld into a classy beatnik joint like in Don Juan in Hell.[5] Or God could repent as he's done in the past and just teleport all of the sinners into heaven.

The whole issue of a so-called unbreakable reward schedule becomes further complicated when talking about the Christian, Mormon, or Muslim interpretation of YHWH. These religions flat-out admit that God unilaterally changed the supposedly unbreakable covenant He gave to earlier worshipers. What exactly, aside from theistspecial pleading, stops God from further altering the deal with his followers?

Furthermore, if you believe in a not-so-omnipotent deity (or a greater-than-omnipotent deity, such as for a simulated reality), there's also no guarantee that at some point in the future paradise and/or perdition won't be destroyed or altered in some form while you're experiencing your 'reward'. Let's see how much you enjoy Valhalla after Hastur annihilates your silly battlefield with its ginormous space tentacles!

Some people consider parts of this scenario to be logically contradictory or incompatible with reality, which leads them to assign a probability of zero to the "Christian hell" outcome.

This may be because they believe that the Christian god is impossible or defined in a contradictory way, because they do not believe such a beneficent god could send anyone to hell, or because they believe that hell itself is impossible. This last argument may be based on the belief that pain requires a physical body, or on an argument that the limited human mind is incapable of suffering eternal torture. If you were tortured for ten times as long as you've been alive, would you be "you" anymore? How about after a million years? A trillion? At some point, whether 10 or 1010 years from now, one would expect that your mind would either break or "get used to it", probably both. Either possibility precludes the experience of infinite regret and suffering.

Unfortunately, a similar argument can be made regarding heaven. An eternal high seems impossible for a limited creature, so going to heaven would only be possible if one transformed into something not only different, but even unrecognizable to one's earthly self; in which case, what's being punished/rewarded isn't meaningfully "you" at all. One must also wonder if eternal bliss is all that it's cracked up to be.

The wager assumes that there is a self-evident reason for rewarding blind faith. Why is the faith of a believer better than the personal courage of the disbeliever that leads an outstanding life? Why does a deity prefer blind faith over evidence based submission?

The real argument goes in the opposite direction: God exists (I assume) and I cannot see him, therefore he has to have a reason not to show himself. Therefore, there has to be something for me if I play along.

If, for the sake of argument, we stack the deck in religion's favor as much as possible, and assume that the only thing that God cares about is whether you believe in him or not, regardless of your other actions, then this implies that God does not value critical thinking, which is a double-edged sword. In this case, those in power could cause all kinds of suffering, justifying it as the will of God, and that it is necessary to bear it in order to get a better reward in heaven. (Indeed, this is already what many fundamentalists believe regarding suffering.) In that case, the costs for the wager are as follows:

God exists

God does not exist

Believe in God

Finite loss from worldly suffering + Infinite gain in heaven

Finite loss from authoritarianism

Disbelieve in God

Finite loss from worldly suffering + Infinite loss in hell

Finite gain from rationalism

Since any finite number added to or subtracted from infinity is infinity, the result simplifies to

God exists

God does not exist

Believe in God

Infinite gain in heaven

Insignificant loss

Disbelieve in God

Infinite loss in hell

Insignificant gain

which is exactly the same as before. Therefore, not even Hyper-Calvinists can successfully use the wager, because of the logical problems listed above.

One way to counter the wager is to replace Pascal's Judeo-Christian God with a perverse god that punishes those who believe in him without evidence, and rewards those who don't. Note that this doesn't even presuppose that the Bible and other holy texts are not divinely inspired: this god could have authored them to serve as a test of credulity. Importantly, because Pascal's Wager can only work if you improve the prior probability of any one god's existence over the others (which generally doesn't happen in any theological argument) this wager is exactly as valid as Pascal's original formulation.

God exists

God does not exist

Believe in God

Infinite loss in hell

Insignificant loss

Disbelieve in God

Infinite reward in heaven

Insignificant gain

This theoretical belief system presents a win/win scenario for atheists and a lose/lose scenario for those who believe in God. Since the two contrasting ideas of a specific god are logically equivalent in likelihood, atheism is shown to have the greatest potential for gain, completely negating and effectively reversing Pascal's argument. Remember, this is equally empirically provable as Pascal's Wager, and so we now have to factor in a 50:50 chance of Pascal's Wager being true or this one being true.

It is dubious whether people can force themselves to believe whatever they want. Instead of considering whether one should believe in God, this reversal considers whether it's a good strategy for an otherwise good, socially responsible person to pretend to believe in God:

God exists

God does not exist

rewards works

rewards faith

Feigning belief

punishment

punishment

finite loss (untruthfulness to self)

Honest disbelief

reward

punishment

finite gain (honest life)

As before, feigning belief is never a better strategy than being honest about your disbelief, unless the punishment for feigned belief (trying to trick a god) is milder than the one for disbelief. True believer is left out, because you're arguing from the viewpoint that belief is something that takes place deep down inside, and is not a facade, and that you simply lack it.

While Pascal's Wager is a theologically flawed argument, the principle has applications in other aspects of life, such as investment and betting - purely because the game theory aspects are reasonable - and Pascal's Wager is brought up by name as an analogy where such gain/loss comparisons can be made. In short, it presents a way of dealing with uncertainty by assessing not probability but only the magnitude of potential gains against losses. In the "global warming wager", the comparison is made between trying to help the environment and not helping the environment. Regardless of whether you believe global warming is a scam or hoax (and regardless of whether you're right), the best outcome is still to protect the environment - aka "what if it's a big hoax and we create a better world for nothing?"

In the Wager, believing in God produces the larger gain whereas not believing produces the greater loses. This principle of comparing potential gains and losses is a way of ensuring against black swan like events ("fragility" and "anti-fragility" according to Black Swan author Nassim Taleb) particularly in economics. For example, placing 100% of your funds into a single investment leads to a possible loss—regardless of the odds, which may be unknowable—of 100% of your funds. Such an event would be a greater loss than if you spread your funds over many investments where a single failure is not devastating but your chances of success are slightly increased. The actual probabilities are irrelevant; it is simply a way of shoring yourself up against the off-chance that you're unlucky. The question asks which route avoids the worst possible outcomes.

The same thinking lies behind solutions to the prisoner's dilemma. Viewing unknown events through the eyes of Pascal's Wager eliminates the need to understand the probabilities behind events because decisions can be made by maximizing potential benefits and minimizing the harms. Indeed, this is the very point of the Wager if it is stripped of its theological implications.

↑ Even in Milton's Paradise LostPandemonium a very happening joint with debate clubs, sex parties, and demon Olympics. At least until all of the human sinners showed up and started wrecking the place with their whining. Then again, John Milton was a dyed-in-the-wool Puritan, so this might have been pretty horrific to him personally.